Periodic GARCH Models Research Articles

Electricity pricing using a periodic GARCH model with conditional skewness and kurtosis components

Abstract This paper extends the investigation of the stochastic properties of electricity price growth rates beyond their first two conditional moments allowing for the impact of seasonality on their parameters. The main contributions include the breakdown of electricity price risk into its pure and skewness price components and the development of a risk neutral forecasting equation for electricity prices. Empirical results using ten-years of hourly wholesale prices from the Day-Ahead electricity market in Germany depict the presence of seasonality, strong mean reversion and up-to third degree time-varying moments.

QMLE of periodic time-varying bilinear– GARCH models

In the current paper, we explore some necessary probabilistic properties for the asymptotic inference of a broad class of periodic bilinear– GARCH processes (P – BLGARCH) obtained by adding to the standard periodic GARCH models one or more interaction components between the observed series and its volatility process. In these models, the parameters of conditional variance are allowed to switch periodically between different regimes. This specification lead us to obtain a new model which is able to capture the asymmetry and hence leverage effect characterized by the negativity of the correlation between returns shocks and subsequent shocks in volatility patterns for seasonal financial time series. So, the goal here is to give in first part some basic structural properties of P – BLGARCH necessary for the remainder of the paper. In the second part, we study the consistency and the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) illustrated by a Monte Carlo study and applied to model the exchange rate of the Algerian Dinar against the US-dollar.

Asymptotic Properties of QML Estimation of Multivariate Periodic CCC − GARCH Models

In this paper, we explore some probabilistic and statistical properties of constant conditional correlation (CCC) multivariate periodic GARCH models (CCC − PGARCH for short). These models which encompass some interesting classes having (locally) long memory property, play an outstanding role in modelling multivariate financial time series exhibiting certain heteroskedasticity. So, we give in the first part some basic structural properties of such models as conditions ensuring the existence of the strict stationary and geometric ergodic solution (in periodic sense). As a result, it is shown that the moments of some positive order for strictly stationary solution of CCC − PGARCH models are finite.Upon this finding, we focus in the second part on the quasi-maximum likelihood (QML) estimator for estimating the unknown parameters involved in the models. So we establish strong consistency and asymptotic normality (CAN) of CCC − PGARCH models.

Mixture periodic GARCH models: theory and applications

This paper discusses mixture periodic GARCH (M-PGARCH) models that constitute very flexible class of nonlinear time series models of the conditional variance. It turns out that they are more parsimonious comparatively to MPARCH models. We first provide some probabilistic properties of this class of models. We thus propose an estimation method based on the expectation-maximization algorithm. Finally, we apply this methodology to model the spot rates of the Algerian dinar against euro and US dollar. This empirical analysis shows that M-PGARCH models yield the best performance among the competing models.

M-estimation for periodic GARCH model with high-frequency data

This paper studies an M-estimator of a proxy periodic GARCH (p, q) scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimator. The numerical results show that our M-estimator is more efficient and robust than other estimators without the use of high-frequency data.

On general periodic time-varying bilinear processes

We study in this note the class of bilinear processes with periodic time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of strict and second order stationary solutions (in periodic sense) and for the existence of higher order moments. The given conditions can be applied to periodic ARMA or periodic GARCH models. The central limit theorem and the law of iterated logarithm (LIL) for higher order sample moments are showed.

A conditional least squares approach to PGARCH and PARMA– PGARCH time series estimation

In this Note, a conditional least squares ( CLS) estimates for periodic GARCH ( PGARCH) models with martingale difference centered squared innovations is developed. The approach is extended to the PARMA– PGARCH models. We establish the strong consistency and the asymptotic normality for our estimate.

On the existence of higher-order moments of periodic GARCH models

In this paper we mainly study the existence of higher-order moments of periodic GARCH models ( P - GARCH) introduced by [Bollerslev, T., Ghysels, E., 1996. Periodic autoregressive conditional heteroskedasticity. Journal of Business and Economic Statistics 14, 139–152]. We provide an explicit necessary and sufficient condition for the existence of higher-order moments for a general P - G A R C H S ( p , q ) model. Our main result generalizes the necessary and sufficient moment condition recently obtained by [Ling, S., McAleer, M., 2002a. Stationarity and the existence of moments of a family of GARCH processes. Journal of Econometrics 106, 109–117; Ling, S., McAleer, M., 2002b. Necessary and sufficient moment conditions for the G A R C H ( p , q ) and asymmetric power G A R C H ( p , q ) models. Econometric Theory 18, 722–729] for the classical G A R C H ( p , q ) models.